The weight of evidence for an extraordinary claim must be proportioned to its strangeness.

We are so far from knowing all the forces of nature and their various modes of action that it would be unworthy of the philosopher to deny phenomena simply because they are inexplicable at the present state of our knowledge. The more difficult it is to acknowledge their existence, the greater the care with which we must study these phenomena.

All the effects of Nature are only the mathematical consequences of a small number of immutable laws.

Truth and justice are the immutable laws of social order.

Such is the advantage of a well constructed language that its simplified notation often becomes the source of profound theories.

The theory of probabilities is basically only common sense reduced to a calculus. It makes one estimate accurately what right-minded people feel by a sort of instinct, often without being able to give a reason for it.

Nature laughs at the difficulties of integration.

Man follows only phantoms.

The most important questions of life are indeed, for the most part, really only problems of probability.

Napoleon: You have written this huge book on the system of the world without once mentioning the author of the universe. Laplace: Sire, I had no need of that hypothesis. Later when told by Napoleon about the incident, Lagrange commented: Ah, but that is a fine hypothesis. It explains so many things.

What we know is not much. What we do not know is immense.

Probability theory is nothing but common sense reduced to calculation.

It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.

The theory of probabilities is at bottom nothing but common sense reduced to calculus it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which of times they are unable to account.

[It] may be laid down as a general rule that, if the result of a long series of precise observations approximates a simple relation so closely that the remaining difference is undetectable by observation and may be attributed to the errors to which they are liable, then this relation is probably that of nature.

The mind has its illusions as the sense of sight and in the same manner that the sense of feeling corrects the latter, reflection and calculation correct the former.

Read Euler, read Euler. He is the master of us all.